Method and system for detecting malfunction of a MEMS micropump

ABSTRACT

Method for detecting failure including possible under or over delivery of a micropump having at least an inlet valve, a pumping chamber with an inner pressure sensor and an outlet valve, said method comprising the determination of the pump tightness via the measurement of the pressure by said inner pressure sensor in said pumping chamber at least at certain intervals when the pump is inactive and the comparison with a value of reference.

This application is a continuation of U.S. application Ser. No.14/128,925 filed Feb. 14, 2014, which is the U.S. national phase ofInternational Application No. PCT/IB2012/053176 filed Jun. 22, 2012,which designated the U.S. and claims priority to EP Application No.11171155.2 filed Jun. 23, 2011 and EP Application No. 11126494.4 filed 4Jul. 2011, the entire contents of each of which are hereby incorporatedby reference.

1. FIELD OF INVENTION

The present invention relates to MEMS (Micro-Electro-Mechanical System)micropumps which may be advantageously used for administrating insulin.Such pumps comprise a pumping chamber having a pumping membrane and anintegrated sensor comprised between two check valves.

More specifically, the present invention concerns the methods formonitoring the state of a MEMS micropump.

2. STATE OF THE ART

The detection of dysfunctions, especially in medical devices, isimportant because the life of the patient may depend on properfunctioning of said devices. In case of infusion pumps, for example, thepotentially dangerous results of a failure are typically over-infusionor under-infusion of the drug into the patient.

Examples of dysfunctions are leaks, occlusions or presence of airbubbles in the pumping line.

State-of-the-art devices and methods for detecting dysfunctions inmedical devices are for instance disclosed in the following patentdocuments: US 2008/214979, EP 1 762 263 and U.S. Pat. No. 7,104,763.

An example of MEMS micropump is disclosed in patent application WO2010/046728. This MEMS micropump 1 as illustrated in FIG. 1 is a highlyminiaturized and reciprocating membrane pumping mechanism. It is madefrom silicon or silicon and glass. It contains an inlet control member,here an inlet valve 2, a pumping membrane 3, a functional inner detector4 which allows detection of various failures in the system and an outletvalve 5. The principle of such micro-pumps is known in the prior art,for example from U.S. Pat. No. 5,759,014.

FIG. 1a illustrates a cross section of a micropump with the stack of aglass layer as base plate 8, a silicon layer as second plate 9, securedto the base plate 8, and a second glass layer 10 as a top plate, securedto the silicon plate 9, thereby defining a pumping chamber 11 having avolume.

An actuator (not represented here) linked to the mesa 6 allows thecontrolled displacement of the pumping membrane 3. A channel 7 is alsopresent in order to connect the outlet control member, the outlet valve5 to the outer detector not represented here and finally to the outletport placed on the opposite side of the pump.

The FIG. 1b illustrates another cross-section of the MEMS micropumpincluding a cover 12 onto the channel 7, the outer detector 13, thefluidic channel 17 between the outer detector 13 and the outlet port 18.

In the pump 1, the pressure inside the pumping chamber varies during apumping cycle depending on numerous factors, such as the actuation rate,the pressure at the inlet and the outlet, the potential presence of abubble volume, the valve characteristics and their leak rates.

Dysfunctions are detected by analysing the pressure profile duringactuation cycles.

The inner pressure sensor 4 and outer pressure sensor 13 in themicro-pump 1 are made of a silicon membrane placed between the pumpingchamber 11 and the pump outlet 5 and between the pump outlet valve 5 andpump outlet port 18 respectively. The sensors are located in a channelformed between the surface of the micro-pumps silicon layer 9 and itstop layer 10. In addition, the sensors comprise a set of strainsensitive resistors in a Wheatstone bridge configuration on themembrane, making use of the huge piezo-resistive effect of the silicon.A change of pressure induces a distortion of the membrane and thereforethe bridge is no longer in equilibrium. The sensors are designed to makethe signal linear with the pressure within the typical pressure range ofthe pump. The fluid is in contact with the surface of theinterconnection leads and the piezo-resistors. A good electricalinsulation of the bridge is ensured by using an additional surfacedoping of polarity opposite to that of the leads and thepiezo-resistors.

Because the analysis methods are performed during actuation (in-strokedetection), the occurrence of events like insulin reservoirpressurization or any other free flow conditions between two strokes arenot detected. At low flow rate hazardous conditions may be thereforedetected too late, leading to severe patient injuries.

There is therefore a need to improve the existing methods and systemsfor detection a malfunction of a MEMS micropump.

3. GENERAL DESCRIPTION OF THE INVENTION

The present invention offers several improvements with respect tostate-of-the-art methods and systems.

The present invention, which may advantageously use the micropumpdescribed in WO 2010/046728 which is inside a device like described inthe application EP11171155.2. The WO 2010/046728 describes out-of-strokedetection methods based on the analysis of at least one integratedpressure sensor. The EP11171155.2 describes medical device whichcomprises three distinct cavities where the pumping element is localisedin the first cavity, the second cavity (which is the reservoir) isdesigned to contain a fluid for delivering to the patient. The first andsecond cavities are separated by a rigid wall while the second and thirdcavities are tightly separated by a movable membrane in such a mannersaid membrane may move between the second and third cavities when thevolume of fluid changes. Said device comprises two distinct ventingmeans, the first one for the first cavity and the second one for thethird cavity. If one of venting means is clogged, the device may over orunder delevry the fluid contained in the reservoir (the second cavity).

Using the method according to the present invention any condition thatinduces a free flow can be detected in few seconds. The amount of overor under delivery can be estimated. The method according to theinvention also allows the detection of reservoir overfilling.

In a preferred embodiment the method according to the invention is basedon the concept of equivalent fluidic resistance of both inlet and outletvalves.

Preferably, the residual fluidic resistances of the valves aredetermined during the last actuation cycle and the real time monitoringof the pressure inside the pumping chamber allows the determination ofthe maximum possible over or under delivery while out-of-stroke.

In-stroke and out-of-stroke detection methods are jointly used to alarmthe patient as soon as possible of the occurrence of a risk of over orunder delivery.

4. DETAILED DESCRIPTION OF THE INVENTION

The invention will be better understood with the following illustratedexamples.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

FIG. 1a illustrates a cross section of a micropump.

FIG. 1b illustrates another cross-section of the MEMS micropump.

FIG. 2 shows a typical pumping cycle having 3 phases.

FIG. 3 shows a schematic fluidic model for the pumping device.

FIG. 4 shows detector signals using the actuation profile given in FIG.2.

FIG. 5 shows detector signals using the actuation profile given in FIG.2.

FIG. 6 shows the maximum flow rate at 37° C.

FIG. 7 shows the max leak rate in U/h.

FIG. 8 shows the pumping device and its different ports,

4.1. PUMP LEAKAGE

The pumping device is made of a reservoir comprising a particle and airfilter, a MEMS micropump 1 having inlet (2) and outlet (5) check-valves,a pumping membrane (3) and integrated detectors (4 and 13) and means toconnect the outlet (18) of the micropump to the patient body includinge.g. a catheter.

All parts of the pumping device which are in contact with insulin definethe fluidic pathway.

We define a leakage as any tightness defect that can lead to an over orunder delivery

We distinguish here two kinds of leakage

1. a leak from the fluidic pathway to outside, due to typically to:

-   -   reservoir failure    -   pumpchip crack    -   septum issues    -   needle issues

2. a leak within the fluidic pathway, due to typically to:

-   -   particles below the valve seats    -   cracks in the valve seats

Leaks towards outside will usually induce under delivery. These kinds ofleakage can be addressed by a test of the fluidic pathway tightnessduring production.

Crackguard rings are also implanted into the pumping membrane, the inletand outlet valves. Any crack in the silicon opens electrically thecrack-guard ring. The mechanical integrity of the movable or sensitivepart of the micropump are therefore tested electrically during thefunctional test but also during the functioning of the device.

Leakage within the fluidic pathway can induce both over and underdelivery.

The tightness of the valves prevents the direct communication betweenthe insulin reservoir and the patient because even during actuationthere is at least one valve normally close in the fluidic pathway. Thepresence of particles below one valve seat induces a back-flow thataffects the pump accuracy. The presence of particles below both valvesassociated with a gradient of pressure between the inlet and the outletinduces a free flow.

Because there is a flow that can potentially transport particles belowthe valve seats, the test of valve tightness should be performedcontinuously while the test of tightness in production is sufficient todetect cracks of the valve seats because this is due to process issuesonly.

The present invention describes both in-production and in-functioningleak detection methods.

4.2. VALVE TIGHTNESS AND EQUIVALENT FLUIDIC RESISTANCE

We consider here a fully working pump unit, i.e. having passed allproduction tests with success. The fluidic pathway is therefore tight aswell as the valves.

It is now important to discuss the notion of tightness because we aretalking about flow rate of only few nanoliters per hour through hardvalve seat having a finite roughness and no compliance.

We characterize a valve normally closed by its finite residual fluidicresistance R_(in) and R_(out), for the inlet and the outletrespectively.

Because the two fluidic resistances are placed in series, there ispotentially a risk a free flow when the sum of their fluidic resistancesR_(in)+R_(out) reaches a threshold value and this independently of theindividual values of R_(in) and R_(out).

After the dry functional test, we characterize the pressure decay fromthe pressurized pumping chamber through the normally close valves placedhere in parallel. We can have therefore access to R_(eq) only which isdefined by:

$R_{eq} = \frac{R_{in}R_{out}}{R_{in} + R_{out}}$

This expression can be written in a more compact way:1/R _(eq)=1/R _(in)+1/R _(out)

R_(eq) is driven by the lowest value between R_(in) and R_(out). Wedefine R_(eq) min as the minimum allowed value during the functionaltest. This value is correlated to the max leak rate Q_(max) allowed bythe design input and by the minimum difference of pressure between theinlet and the outlet ΔP_(th) that can be detected by the pressuresensor.

The maximum leak rate is defined by:

$Q_{\max} = \frac{\Delta\; P_{th}}{R_{in} + R_{out}}$

For a given value of R_(eq) and ΔP_(th), the minimum value of the sumR₁₀₁=R_(in)+R_(out) is obtained for R_(in)=R_(out)=2 R_(eq) asdemonstrated below:

$R_{tot} = {{R_{in} + R_{out}} = \frac{R_{in}R_{out}}{R_{eq}}}$

Then

$R_{tot} = \frac{R_{out}^{2}}{R_{out} - R_{eq}}$

The function R_(tot) is minimal for a value of R_(out) that nullifiesthe derivative:

$\frac{\partial R_{tot}}{\partial R_{out}} = 0$

We get2R _(out)(R _(out) −R _(eq))−R _(out) ²=0

And finally R_(tot) is minimized forR _(out) =R _(in)=2R _(eq)

In the worst case, the max leak rate Q_(max) between the inlet and theoutlet of the pump unit, for the pressure gradient ΔP_(th), is finally:

$Q_{\max} = \frac{\Delta\; P_{th}}{4\; R_{eq}}$

To summarize, we define a pump unit as tight a pump unit having passedwith success the dry test using the min value of R_(eq min) for theequivalent fluidic resistances of the leak. This pump unit will exhibitin the worst case a max leak of Q_(max) under the pressure gradientΔP_(th) which corresponds to the minimum difference of pressure that canbe detected by the integrated sensor.

4.3. VALVE TIGHTNESS AND PATIENT SAFETY

We simply review here the basic concepts around the valve tightness asan introduction to the detection methods.

To generate a leak (defined here as a flow from the reservoir to thepatient) two elements are necessary:

-   -   a leaky fluidic pathway    -   a gradient of pressure.        Origin of the Finite Fluidic Resistance of the Valve

When the pump is not actuated, the system can be considered as apressurized reservoir at the pressure P_(in), which is connected to thepatient at the pressure P_(out) through two check valves having a finiteresidual fluidic resistance, a dead volume and a small elasticity inbetween.

Because the valve seats are not compliant to rigid particles, the riskof permanent opening shall be considered. The use of filter thereforelimits the occurrence of a particle contamination but we cannot excludeparticle release from the filter of the device itself or simply thedisplacement of a particle, which would be already present in the pump,below the valve seat during actuation. Leaks due to defect of the valveseats or defect of the bonding are detected during the functional testand are not considered here.

Pressure Gradient

In normal conditions P_(in) is null or slightly negative by design: thereservoir is made of a thermoformed plastic soft pouch is soldered ontoa hard shell; a small negative pressure is therefore needed to bucklethe soft pouch towards the hard shell because of its dedicated shape.The range is typically 0/−10 mbar.

The pressure of the patient can be considered as null or slightlynegative (−0.9+/−1.7 mbar according to E. Stranden and H. O. Myhre,Microvascular Research 24, 241-248 (1982), and −2.6 mbar according toGuyton and Hall, Textbook of Medical Physiology, Saunders Elsevier,twelfth edition (2011).

The additional pressure due to the water column height shall beconsidered. For patch device the maximum head height is few cm, inducingonly few mbar between the reservoir and the patient.

In normal conditions the pump unit is safe because over infusion isprevented by the small and negative gradient of pressure between thereservoir and the patient.

We consider now deviations from the normal conditions: we can haveoverpressure in the reservoir due to an overfilling or due to acompression of the pumping unit external shell that should pressurizethe reservoir. The pump unit should be able to detect any reservoirpressure conditions that make potential leakage hazardous for thepatient even if no leakage is observed because this is an abnormalsituation. The reservoir hard shell design is made to prevent thetransmission of pressure to the reservoir soft pouch. The pump unittriggers an alarm when the pressure sensor in the pump “sees” areservoir pressure larger than ΔP_(th) mbar. This pressure should bemonitored in real time to alarm as soon as possible the patient ofabnormal conditions.

Leak Detection, Back Flow and Free Flow

Valve leakage could induce:

-   -   I. A back flow    -   II. A free flow

A back flow is a leak induced under infusion during actuation in normalconditions. A leak at the inlet (outlet) induces a backflow duringexpulsion (suction) phase. These backflows corresponds in all cases toan under infusion. An alarm should be ideally triggered when thecriterion on the pumping accuracy is not met. It is important to notethat for the delivery accuracy it is no longer important to know if theinlet or the outlet or both are leaking. A criterion based on theequivalent fluidic resistance of the leak is enough to evaluate theinfusion error due to leakage.

A free flow is a flow in delivery pathway which is not controlled by thepumping unit. A free flow is therefore an under or over infusion fromthe reservoir to the patient due to valve leakages out ofspecifications. Because the valves are placed in series both valvesshould exhibit a significant leak. As discussed previously abnormalpressure conditions should be also present to induce the flow.

To get a valve opening of 0.5 um for instance, it is necessary to haveseveral spherical hard particles of 0.5 um onto the valve seat. Thepresence of only one particle induces a tilt of the valve that reducessignificantly the fluidic resistance as illustrated below. Only oneparticle of 0.8 um onto the valve seat is equivalent to a valve apertureof 0.5 um.

The valves have also the capability to compress soft particles. In thepresent invention the worst case would be considered for analyticalcalculations: a particle of x um generates an opening of x um. Soft ornon-spherical particles are not considered.

4.4. IN-STROKE LEAK DETECTION PRINCIPLE

The in-stroke leak detection principle is based on the analysis of thepressure decay within the pumping chamber after actuation. Thesensitivity of the method is due to the very low elasticity of thepumping chamber coupled to its very low dead volume.

A typical pumping cycle has 3 phases according to FIG. 2:

-   -   1) “A” is a ½ push of the pumping membrane starting for the rest        position located between the two stop limiter towards the upper        limiter (infusion)    -   2) “B” is a full pull of the pumping membrane from the upper to        the lower stop limiter (filling)    -   3) “C” is a ½ push of the pumping membrane from the lower        limiter to the rest position (“R”) (infusion)

After the first or the third ½ push phases, the pressure in the pumpingchamber is positive and equal to the outlet valve pretension for tightvalves (+P_(val out).

After the second pumping phase (filling), the pressure in the pumpingchamber is negative and equal to the inlet valve pretension for tightvalves (−P_(val in)).

The residual valve leakages induce a pressure decay that can be analyzedto determine their equivalent fluidic resistances R_(eq). For very largeleakage the backflow is too large to generate any pressure in thepumping chamber and the pressure remains constant.

When the pumping membrane is against a stop limiter (after the cycles 1and 2), the elasticity of the pumping chamber is only limited to thedetector membrane elasticity and the secondary deformation of thepumping and outlet membrane due to the pressure.

When the pumping membrane is located at its rest position without anyvoltage on the piezo actuator, the pumping chamber shows a much largerelasticity due to the pumping membrane at its rest position even byconsidering the stiffening induced by the short-circuited actuatortightly linked to it.

In all cases the presence of bubbles should be considered for theestimation of the elasticity.

The pressure decay after the phases 1 and 2 are therefore expected to bevery fast while after the phase 3 we expect a slow decay.

We will focus on the analysis of the pressure decay after the phase 1 or2.

4.5. ANALYTICAL MODEL

We distinguish two different methods for the leak detection: the drytest method, based on the analysis of the air pressure decay during afunctional test, and the wet method used during the functioning of thepump. In both cases we should estimate the elasticity of the system. Forthe dry test we should focus on the air compressibility and the methodis described firstly. For the wet test, because of the very lowcompressibility of the water, the elasticity of the pump is relevant. Weprovide therefore an estimation of the pumping chamber elasticityincluding potential bubbles and describe finally the in-functioning leakdetection model.

FIG. 3 shows a schematic fluidic model for the pumping device.

Leak Detection During Dry Test

The method is based on the pressure decay analysis in the pumpingchamber after a compression and a blocking of the outlet valve which isobtained by applying a large pressure onto its vent.

We consider therefore an isothermal compression which reduces thepumping chamber volume from V_(S)+V_(D) to V_(D), where V is the strokevolume and V_(D) is the dead volume.

We note n(t) the number of mole of gas and V the volume of the pump atthe time t.

The total differential of the pressure is:

${dP} = {{\left( \frac{\partial P}{\partial n} \right)_{V}{dn}} + {\left( \frac{\partial P}{\partial V} \right)_{n}{dV}}}$

We obtain, using the ideal gas law:

$\frac{dP}{P} = {\frac{dn}{n} - \frac{dV}{V}}$

In this expression, dn is the variation of the number of gas moles dueto the isothermal flow and dV is the variation of volume due to theelasticity of the pump.

The variation of volume of the pump with the pressure is mainly due tothe deformation of the different membranes (detector, actuation, outletvalve). We assume that this variation is linear:V=V ₀+α_(g)(P−P ₀)

A variation of dP induces a variation of volume:dV=α _(g) dP

The quantity dn is related to the net flow Q during dt:

$\frac{dn}{n} = {\frac{Q}{V}{dt}}$

We obtain:

$\frac{dP}{dt} = {\frac{PQ}{V + {\alpha_{g}P}} = \frac{Q_{in} + Q_{out}}{\alpha_{g} + \frac{V}{P}}}$

The flows Q_(in) and Q_(out) are respectively the inflow and outflow inthe pump.

For the dry test, we assume that the elasticity of the pump can beneglected when the pump is in contact with a stop limiter. The volume Vis therefore constant and equal to V_(D).

The former equation writes:

${dt} = {{{- R_{eq}}V_{D}\frac{dP}{P\left( {P - P_{0}} \right)}} = {\frac{R_{eq}V_{D}}{P_{0}}\left( {\frac{1}{P} - \frac{1}{P - P_{0}}} \right){dP}}}$

This equation can be easily solved and we obtain:

$P = \frac{P_{0}}{1 - {\left( {1 - \frac{P_{0}}{P_{\max}}} \right){{Exp}\left\lbrack {- \frac{P_{0}\left( {t - t_{0}} \right)}{R_{eq}V_{D}}} \right\rbrack}}}$

Where P_(max) is the max pressure obtained at the end of the compressionof the pumping chamber.

We note τ_(1/2) the time necessary to reduce the relative pressure by afactor 2:

$\tau_{1/2} = {\frac{R_{eq}V_{D}}{P_{0}}{\ln\left\lbrack {1 + \frac{P_{0}}{P_{\max}}} \right\rbrack}}$

Typical values:

R_(eq min)=4E16 Pa·s/m⁻³.

For nitrogen the value of R_(eq min) is divided by 57 according to itsviscosity.

If the criterion is verified, the max flow rate for water at 37° C., inthe worst case, would be 0.032 ul/h for a pressure gradient of 100 mbar.

Elasticity of the System

Considering wet leak test, the elasticity of the pump α shall beincluded into the model.

The volume V(P) of the pump takes the form:V(P)=V ₀+α(P−P ₀)=V _(liquid) +V _(bubble)(P)

Where V₀ is the volume of the pump at P=P₀.

Because of the very low compressibility of water we neglect the volumechange of the liquid with the pressure.

The elasticity of the different parts of the pump is estimated hereincluding the bubbles.

Pumping Membrane

If the membrane is in contact against a stop limiter, the membrane onlyundergoes a secondary distortion by applying pressure.

Typical Values

ΔV_(membrane)=0.135 nl/100 mbar

α_(membrane)=1.35E−17 m³/Pa

If the pumping membrane is at its rest position, the elasticity is nowdriven by the membrane and the piezo bender.

The elasticity of the pumping membrane in that configuration istypically:

ΔV_(membrane)=8.28 nl/100 mbar

α_(membrane)=8.28E−16 m³/Pa

Detector

Typical Values

ΔV_(detector)=0.25 nl/100 mbar

α_(detector)=2.5E−17 m³/Pa

Outlet

The outlet valve is a circular membrane which shows the followingtypical elasticity if closed:

ΔV_(outlet)=0.096 nl/100 mbar

α_(outlet)=9.6E−18 m³/Pa

Pump Elasticity

When the pumping membrane is in contact with the stop limiters, when thevalves are closed and when there is no bubble, the overall pumpelasticity is the sum of the elasticity of the pumping membrane, thedetector and the outlet membrane as shown in FIG. 4:

ΔV_(pump)=0.48 nl/100 mbar

α=4.8E−17 m³/Pa

When the piezo is not powered, the elasticity of the pump is mainlygoverned by the elasticity of the pumping membrane:

ΔV_(pump)=8.625 nl/100 mbar

α=8.625E−16 m³/Pa

Bubbles

According to the ideal gas law, we have:

${V_{bubble}(P)} = {{V_{b}(P)} = {\frac{P_{0}}{P}V_{b\; 0}}}$

Where P is the absolute pressure and V_(bo) the volume of the bubble atP=P₀.

We note P=P₀+P′ where P′ is the relative pressure.

If P′«P₀ we can do the following approximation that simplifies themodel:

$\frac{P_{0}}{P} = {\frac{1}{1 + \frac{P^{\prime}}{P_{0}}} \approx {1 - \frac{P^{\prime}}{P_{0}}} \approx {1 - \frac{P - P_{0}}{P_{0}}}}$

We obtain:

${{V_{b}(P)} \approx {V_{b\; 0}\left( {1 - \frac{P - P_{0}}{P_{0}}} \right)}} = {V_{b\; 0} + {\alpha^{\prime}\left( {P - P_{0}} \right)}}$${{W{ith}}\mspace{14mu}\alpha^{\prime}} = {- \frac{V_{b\; 0}}{P_{0}}}$

4.6. IN-FUNCTIONING LEAK DETECTION/WET LEAK DETECTION

For the test of pressure decay, the system can be seen as a pumpingchamber at a pressure P with two fluidic resistances in parallelconnected respectively to a pressure reservoir at P_(in) and P_(out)according to FIG. 3.

Volume of Liquid V_(liq) in the Pumping Chamber

We consider all contributions to the system elasticity in the case of apumping membrane being in contact with a stop limiter and the two valvesbeing closed.

We have therefore:V _(liquid) =V ₀+α(P−P ₀)−V _(b) =V ₀+α(P−P ₀)−V _(b0)−α′(P−P ₀)Expression of the Pressure Decay

In order to estimate the evolution of the pressure just after the end ofa stroke, i.e. when the relative pressure in the pumping chamber isequal to the inlet pretension (after a fill) or the outlet pretension(after an infusion), we simply write the equation of the matterconservation:

${Q + \frac{{dV}_{liquid}}{dt}} = 0$

We can write, since the flow is laminar:

$Q = {{- \frac{{dV}_{liquid}}{dt}} = {{\frac{P - P_{0} - P_{in}^{\prime}}{R_{in}} + \frac{P - P_{0} - P_{out}^{\prime}}{R_{out}}} = {{{- \left( {\alpha - \alpha^{\prime}} \right)}\frac{dP}{dt}} = {\frac{P - P_{0}}{R_{eq}} - \frac{P_{in}^{\prime}}{R_{in}} - \frac{P_{out}^{\prime}}{R_{out}}}}}}$

Where P_(in)′ and P_(out)′ are relative pressures

$\quad\left\{ \begin{matrix}{P_{in} = {P_{0} + P_{in}^{\prime}}} \\{P_{out} = {P_{0} + P_{out}^{\prime}}}\end{matrix} \right.$

We note

$ɛ = \frac{R_{in}}{R_{out}}$$\chi = {\frac{P_{in}^{\prime}}{R_{in}} + \frac{P_{out}^{\prime}}{R_{out}}}$$\xi = {{\chi\; R_{eq}} = {\frac{P_{in}^{\prime}}{1 + ɛ} + \frac{P_{out}^{\prime}}{1 + \frac{1}{ɛ}}}}$$\lambda = \frac{1}{R_{eq}\left( {\alpha - \alpha^{\prime}} \right)}$Andβ = P_(out)^(′) + P_(val  out) − χ R_(eq) = P_(out)^(′) + P_(val  out) − ξ

Thus

${\chi\; R_{eq}} = {\frac{P_{in}^{\prime}}{1 + ɛ} + \frac{P_{out}^{\prime}}{1 + \frac{1}{ɛ}}}$

We obtain:

$\frac{dP}{P - P_{0} - {\chi\; R_{eq}}} = {{- \frac{dt}{R_{eq}\left( {\alpha - \alpha^{\prime}} \right)}} = {{- \lambda}\;{dt}}}$

Thus

${\ln\left( {P - P_{0} - {\chi\; R_{eq}}} \right)} = {{- \frac{t - t_{0}}{R_{eq}\left( {\alpha - \alpha^{\prime}} \right)}} + v}$

Where ν is an integration constant.

During the infusion, just after the push move of the membrane (i.e. whenthe outlet valve closes) the pressure in the pumping chamber is equalto:P(t ₀)−P ₀ =P _(out) ′+P _(vol out) =χR _(eq) +e ^(ν)

Finally the expression of the relative pressure P−P₀ in the pumpingchamber takes the form:

${P - P_{0}} = {{{\chi\; R_{eq}} + {\left( {P_{out}^{\prime} + P_{{val}\mspace{14mu}{out}} - {\chi\; R_{eq}}} \right)e^{- \frac{t - t_{0}}{R_{eq}{({\alpha - \alpha^{\prime}})}}}}} = {\xi + {\beta\; e^{- {\lambda{({t - t_{0}})}}}}}}$  Or${P - P_{0}} = {\frac{P_{in}^{\prime}}{1 + ɛ} + \frac{P_{out}^{\prime}}{1 + \frac{1}{ɛ}} + {\left( {P_{out}^{\prime} + P_{{val}\mspace{14mu}{out}} - \frac{P_{in}^{\prime}}{1 + ɛ} - \frac{P_{out}^{\prime}}{1 + \frac{1}{ɛ}}} \right)e^{- \frac{{({t - t_{0}})}{({1 + ɛ})}}{R_{in}{({\alpha - \alpha^{\prime}})}}}}}$

During the time τ after t₀, the total volume of liquid ΔV_(liq) thatflows outside the pumping chamber is:

${\Delta\; V_{liq}} = {{{\int_{t_{0}}^{t_{0} + \tau}{\frac{P - P_{0} - P_{in}^{\prime}}{R_{in}}{dt}}} + {\int_{t_{0}}^{t_{0} + \tau}{\frac{P - P_{0} - P_{out}^{\prime}}{R_{out}}{dt}}}} = {\int_{\tau}{{dt}^{\prime}\left\lbrack {\frac{\xi - P_{in}^{\prime} + {\beta\; e^{{- \lambda}\; t}}}{R_{in}} + \frac{\xi - P_{out}^{\prime} + {\beta\; e^{{- \lambda}\; t}}}{R_{out}}} \right\rbrack}}}$

Finally we obtain

$V_{tot} = {\frac{\beta}{\lambda}\left( \frac{1 - e^{{- \lambda}\;\tau}}{R_{eq}} \right)}$Pressure Leak Threshold

We set the leak alarm threshold at the relative pressure P_(leak) and wecan estimate, according to the environment conditions and the devicecharacteristics, the duration τ_(leak) necessary to reduce the pumpingchamber pressure from the relative pressure P_(val out) towards P leakis:

$\tau_{leak} = {{- \frac{1}{\lambda}}{\ln\left\lbrack \frac{P_{leak} - \xi}{\beta} \right\rbrack}}$

It is therefore possible to simulate the duration τ_(leak) by varyingall parameters of the previous formula according to their respectiveranges.

In the following detailed form, it is possible to see all terms thataffect τ_(leak):

$\tau_{leak} = {{- {R_{eq}\left( {\alpha - \alpha^{\prime}} \right)}}{\ln\left\lbrack \frac{P_{leak} - {R_{eq}\left( {\frac{P_{in}^{\prime}}{R_{in}} + \frac{P_{out}^{\prime}}{R_{out}}} \right)}}{P_{out}^{\prime} + P_{{val}\mspace{14mu}{out}} - {R_{eq}\left( {\frac{P_{in}^{\prime}}{R_{in}} + \frac{P_{out}^{\prime}}{R_{out}}} \right)}} \right\rbrack}}$

Considering the in-functioning criterion for the leak rate, we comparethe measured duration τ_(leak mes) to a specification τ_(spec): thedevice is acceptable in term of leak rate ifτ_(leak mes)≥τ_(spec)Leak Criterion Based on the Worst Case Conditions of Free Flow:In-Stroke Detection

The in-functioning leak test gives an indication of the equivalentfluidic resistance of the valve leaks R_(eq).

We measure τ_(leak mes) and we would like to know in the worst case whatis the biggest leak rate associated to that measurement.

-   -   1. We determine first the conditions necessary to obtain the        lowest R_(eq) corresponding to τ_(leak mes) and we derive R_(eq)    -   2. We determine the worst configuration for R_(in) and R_(out)        according to R_(eq)    -   3. We determine the max leak rate Q_(max) from the reservoir        towards the patient in the worst case

For a given R_(eq), the max leak from the reservoir to the patient ismet for:

R_(out) = R_(in) = 2 R_(eq)$R_{eq} = {- \frac{\tau_{{leak}\mspace{14mu}{mes}}}{\left( {\alpha - \alpha^{\prime}} \right){\ln\left\lbrack \frac{P_{leak} - \frac{P_{in}^{\prime}}{2} - \frac{P_{out}^{\prime}}{2}}{P_{{val}\mspace{14mu}{out}} + \frac{P_{out}^{\prime}}{2} - \frac{P_{in}^{\prime}}{2}} \right\rbrack}}}$

The measurement of R_(eq) depends on the pressure conditions at theinlet and the outlet as well as the quantity of air inside the pumpingchamber. The detector launches an alarm when the pressure in thereservoir exceeds P_(in th) and when the bubble in the pump exceedV_(b th) (with the corresponding value of α′_(th)). We assume that thepressure at the outlet is null.

Thus

$R_{eq} = {- \frac{\tau_{{leak}\mspace{14mu}{mes}}}{\left( {\alpha - \alpha_{th}^{\prime}} \right){\ln\left\lbrack \frac{P_{leak} - \frac{P_{{in}\mspace{14mu}{th}}^{\prime}}{2}}{P_{{val}\mspace{14mu}{out}} - \frac{P_{{in}\mspace{14mu}{th}}^{\prime}}{2}} \right\rbrack}}}$

As discussed before, in the worst case, the max leak rate from thereservoir to the patient that can be obtained for a given R_(eq) is:

$Q_{\max} = {\frac{\Delta\; P_{th}}{4\; R_{eq}} = {{- \frac{P_{{in}\mspace{14mu}{th}}^{\prime}}{4\;\tau_{{leak}\mspace{14mu}{mes}}}}\left( {\alpha - \alpha_{th}^{\prime}} \right){\ln\left\lbrack \frac{P_{leak} - \frac{P_{{in}\mspace{14mu}{th}}^{\prime}}{2}}{P_{{val}\mspace{14mu}{out}} - \frac{P_{{in}\mspace{14mu}{th}}^{\prime}}{2}} \right\rbrack}}}$

Where ΔP_(th) is the max gradient of pressure between the inlet and theoutlet that can be present without launching an alarm.

We have therefore associated a maximum leak rate, according to the worstexternal conditions to the measured value of τ_(leak mes).

It is now possible to associate the specification in term of leak rateof the design input with a value of τ_(leak max DI):

$Q_{\max\mspace{14mu}{DI}} = {{- \frac{P_{{in}\mspace{14mu}{th}}^{\prime}}{4\;\tau_{{leak}\mspace{14mu}\max\mspace{14mu}{DI}}}}\left( {\alpha - \alpha_{th}^{\prime}} \right){\ln\left\lbrack \frac{P_{leak} - \frac{P_{{in}\mspace{14mu}{th}}^{\prime}}{2}}{P_{{val}\mspace{14mu}{out}} - \frac{P_{{in}\mspace{14mu}{th}}^{\prime}}{2}} \right\rbrack}}$

In that configuration, if τ_(leak mes)≥τ_(leak max DI), we can ensure at100% that the device is safe. If this criterion is too conservative,Monte Carlo simulations are desirable to determine a good trade-offbetween safety and false alarm rating.

To illustrate this point we propose the following numerical application:

P_(leak)=50 mbar

P_(in th′)=50 mbar

P_(val out)=110 mbar

α=4.8E−17 m³/Pa

bubble size threshold=10 nl

⇒α′=−1E−16 m³/Pa

Q_(max DI)=0.179 U/h

⇒τ_(leak max DI)=0.455 s

The time necessary to reduce the relative pressure by a factor 2 (i.e.from 100 to 50 mbar) is therefore 0.455 s according to these worstconditions.

Without bubbles, this time constant is only 0.148 s.

In normal conditions of pressure, the max gradient of pressure is 18.6mbar.

We obtain:

τ_(leak max DI)=0.1254 s with bubble of 10 nl

τ_(leak max DI)=0.041 s without bubble

The analytical model can be used to determine τ_(spec) value that isacceptable in term of risk for the patient and that will launch too muchfalse alarm: a high value of τ_(spec) is conservative in term of patientsafety but the too high number of false alarm is not acceptable in termof usability.

The opposite situation with a small τ_(spec) is no longer acceptablebecause true alarms will be missed.

Leak Criterion Based on the Pumping Accuracy

Without any upstream or downstream pressure, a leak can induce abackflow that reduces the net pumped volume.

In bolus mode, we assume in a first approximation that the mean pressureduring the positive or negative peak of pressure is +/−Pmax mbar duringa maximum duration of T ms.

We assume a backflow at the inlet. The backflow can be determined byintegrating the pressure profile and by dividing this by the fluidicresistance of the backflow Rf_(backflow).

Typical Values:

Rf_(backflow)=4E14 Pa·s/m³.

This corresponds to a typical opening of about 1 to 1.5 um.

Since R_(eq)≈R_(backflow) we obtain:

$\tau_{leak} = {{- {R_{eq}\left( {\alpha - \alpha^{\prime}} \right)}}{\ln\left\lbrack \frac{P_{leak}}{P_{{val}\mspace{14mu}{out}}} \right\rbrack}}$Using P_(leak) = 50  mbar P_(val  out) = 100  mbar α = 4.8 E − 17  m³/Pabubble  size  threshold = 10  nl ⇒ α^(′) = −1 E − 16  m³/Pa

We obtain

⇒τ_(leak)=0.041 s

During the infusion, the pressure shows a peak of pressure and afterabout 100 ms the pressure should be more or less equal to the outletvalve pretension. If the pressure decay is fast enough to reduce thispressure by a factor 2 in less than 41 ms, then we expect in this worstcase an error on the accuracy larger than 5%.

Without bubble, this time is divided by 3, leading to a quasiinstantaneous pressure release to P₀ after the actuation (less than 13.6ms).

We can conclude that the criterion on the delivery accuracy is mucheasier to be met than the criterion on the leakage.

This estimation shows that we should consider the leak criterion basedon the free flow and not on the back flow.

The FIG. 5 shows typical detector signals using the actuation profilegiven in FIG. 2 for a tight pump (bold line) and a pump having a backflow of 15% (thin line).

According to the examples provided above the fast pressure decay afteractuation is very fast in presence of back flow.

4.7. LEAK DETECTION AND STATIC PRESSURE MEASUREMENT: OUT-OF-STROKEDETECTION

At slow basal rate, the pressure in the pumping chamber shall bemonitored to check eventual reservoir over or under pressure.

To investigate the effect of a static pressure at the inlet, we assumethat in case of constant inlet pressure, the valves are either togetheropen or together closed.

We distinguish therefore two cases:

-   -   1. P−P_(out)>P_(val out)    -   2. P−P_(out)<P_(val out)        Case 1: Static Pumping Chamber Pressure>Outlet Valve Pretension

In the case 1, because the outlet valve is open, the inlet valve isautomatically open and the inlet pressure is therefore larger thanP_(val in)+P_(val out)+P₀. In that configuration of large overpressure(larger than the sum of the valve pretensions) the flow is very large.We assume that the fluidic resistances of the valves are equivalent inthat configuration. To estimate the max flow rate, we only consider thefluidic resistances of the valves and we do not consider singular headlosses.

The FIG. 6 shows the typical maximum flow rate at 37° C. using theformer approximation:

The pressure P in the pumping chamber is here the half of the inletpressure.

Case 2: Static Pumping Chamber Pressure<Outlet Vale Pretension

The pump is in basal configuration. During the last stroke theequivalent fluidic resistance of the valves has been estimated and thereis no alarm and no inlet overpressure.

We suppose the inlet pressure rises to a value P_(in). The pressure inthe pumping chamber is equal to P with P<100 mbar. In this configurationboth valves are closed. We can assume that from the last stroke theresidual leaks of the valves do not change. The equivalent fluidicresistance R_(eq) of the valves is therefore known.

We try to estimate in the worst case what is the max free flow Q_(max)for a measured value of P and a given value of R_(eq).

We have already shown that for a given P_(in) and a given R_(eq), themax flow rate is obtained when

${P_{in} - P_{0}} = \frac{P - P_{0}}{2}$

This rule is unfortunately not reciprocal.

The max inlet pressure is equal to P+P_(val in) (otherwise the inletvalve is open in contradiction to the discussion hereabove).

We will now use the max leak rate theorem.

Max Leak Rate Theorem

If P−P₀<P_(val out), and for a given R_(eq) of the valves, the max leakrate is obtained for P_(in)=P+P_(val in)

This theorem is demonstrated using a proof by contradiction.

Demonstration:

We consider a system having a pressure P in the pumping chamber, anequivalent fluidic resistance of the valves R_(eq) and a pressureP_(in)<P+P_(val in) inducing a leak rate Q.

We will show that for any increase of inlet pressure δP_(in) from anyP_(in) up to P+P_(val in) there is always a couple of values R_(in) andR_(out) values that keeps constant R_(eq) and P and that lead to a flowrate larger than Q.

We have:

$\quad\left\{ \begin{matrix}{Q = {\frac{P_{in} - P_{0}}{R_{in} + R_{out}} = \frac{P - P_{0}}{R_{out}}}} \\{and} \\{Q^{\prime} = {\frac{P_{in} + {\delta\; P_{in}} - P_{0}}{R_{in}^{\prime} + R_{out}^{\prime}} = \frac{P - P_{0}}{R_{out}^{\prime}}}}\end{matrix} \right.$

We will show that there are values R′_(in) and R′_(out) that ensure thatQ′>Q.

$R_{eq} = {\frac{R_{in}R_{out}}{R_{in} + R_{out}} = {\frac{R_{in}^{\prime}R_{out}^{\prime}}{R_{in}^{\prime} + R_{out}^{\prime}} = {\frac{R_{in}}{1 + ɛ} = {\frac{R_{in}^{\prime}}{1 + ɛ^{\prime}} = {\frac{R_{out}}{1 + \frac{1}{ɛ}} = \frac{R_{out}^{\prime}}{1 + \frac{1}{ɛ^{\prime}}}}}}}}$

With

$\quad\left\{ \begin{matrix}{ɛ = {\frac{R_{in}}{R_{out}} = {\frac{P_{in} - P_{0}}{P - P_{0}} - 1}}} \\{ɛ^{\prime} = {\frac{R_{in}^{\prime}}{R_{out}^{\prime}} = {\frac{P_{in} + {\delta\; P_{in}} - P_{0}}{P - P_{0}} - 1}}}\end{matrix} \right.$

We obtain:

$\mspace{20mu}{R_{in}^{\prime} = {{\left( {1 + \frac{\delta\; P_{in}}{P_{in} - P_{0}}} \right)R_{in}} > R_{in}}}$  And$R_{out}^{\prime} = {{\frac{\left( {P_{in} - P} \right)}{\left( {P_{in} + {\delta\; P_{in}} - P} \right)} \times \frac{\left( {P_{in} - P_{0} + {\delta\; P_{in}}} \right)}{\left( {P_{in} - P_{0}} \right)}R_{out}} = {\frac{1 + \left( \frac{\delta\; P_{in}}{P_{in} - P_{0}} \right)}{1 + \left( \frac{\delta\; P_{in}}{P_{in} - P} \right)}R_{out}}}$

For P>P₀ we check that R′_(out)<R_(out) as expected for Q′>Q.

We have therefore demonstrated that the max flow is obtained forP_(in)=P+P_(val in).

The max leak rate takes the form:

$Q_{\max} = {\frac{P + P_{{val}\mspace{14mu}{in}} - P_{0}}{R_{in} + R_{out}} = \frac{P - P_{0}}{R_{out}}}$

The max flow rate is obtained for:

$ɛ = {\frac{R_{in}}{R_{out}} = \frac{P_{{val}\mspace{14mu}{in}}}{P - P_{0}}}$

Finally, the max leak rate, for a given R_(eq) and a given staticpressure P in the pumping chamber, takes the form:

$Q_{\max} = {\frac{P - P_{0}}{R_{eq}\left( {1 + \frac{P - P_{0}}{P_{{val}\mspace{14mu}{in}}}} \right)} = \frac{1}{R_{eq}\left( {\frac{1}{P - P_{0}} + \frac{1}{P_{{val}\mspace{14mu}{in}}}} \right)}}$

We can compare the accuracy of this out-of-stroke leak detection withthe in-stroke detection as described hereabove.

We consider now an in-stroke detection threshold of 50 mbar leading to amax leak rate of 0.179 U/h: we obtain R_(eq)=2.514E15 Pa·s/m³.

The FIG. 7 shows the max leak rate in U/h that can be detected usingin-stroke and out-of-stroke detection as a function of the detectionpressure threshold:

The measurement of the inner detector to check a possible inletoverpressure is mandatory. The main issue of this measurement is thatthe inner detector is not sensitive to inlet pressure lower than 100mbar if the ratio

$ɛ = \frac{R_{in}}{R_{out}}$is large. This effect is due to the inlet valve pretension. During thestroke, the inlet valve opens and the detector directly “sees” thereservoir pressure.

Even if the out-of-stroke detection of the leak is two at four timesless sensitive than during a stroke, this method gives fundamentalimprovement in term of patient safety because of the continuousestimation of the maximum leak rate in the worst case, withoutadditional stroke and with limited power consumption.

To summarize, the monitoring of the inner (4) and outer (13) detectorsignals, when the pump is not actuated, is used to detect under or overpressure onto the reservoir and to estimate the related maximum over orunder infusion.

4.8. STATIC LOAD ON RESERVOIR HOUSING

Static load could be detected by the pressure sensors without actuatingthe pump if it results:

1. an increase of the reservoir pressure

2. or an increase of the interstitial pressure

If the static load transmits a force directly onto the reservoirmembrane, the reservoir pressure increases as well as the downstreampressure according to the discussion here above. A static measurement ofthe inner pressure sensor (4) is used to detect the effect of the staticload.

If the static load transmits a force directly onto the patient skinaround the cannula, typically for patch pump, the tissue compressionwill increase the interstitial pressure and therefore the pressure atthe pump outlet (18) because the insulin will transmit this pressure.The two pressure sensors (4 and 13) and more especially the sensor (13)at the outlet of the pump will directly see this pressure increase.

4.9. VENT CLOGGING

The first and third cavities (described in the application EP11171155.2)have venting means to prevent any pressurization. If one of said ventingmeans get clogged, the pressure gradient between inside device andexternal environment may change inducing an over or under delivery.

The FIG. 8 shows the pumping device and its different ports. The inletvalve port (21) is connected to the reservoir wherein a pressure formthe reservoir (“P_(r)”). The outlet valve port (25) is connected to thepatient wherein a pressure form the patient (“P_(p)”). The membrane port(22), the inner detector port (23) and the outer detector port notrepresented here are connected to the pump controller that includes theactuator wherein a pressure (“P_(pc)”). The outlet valve has a specificventing port 24 which is used during functional test as described in thedocument WO 2010/046728.

In another embodiment, the document WO2007113708 shows for instance apumping device wherein the reservoir and the pump controller (actuator,driving electronics and batteries) share the same venting hole towardsoutside.

In case of vent clogging, a positive or negative pressure may be trappedin the reservoir housing and/or in the pump controller.

The change of pressure due to clogging can be monitored using the twosensors of the pump even without actuation.

Vent Clogging Case Studies:

-   -   1. clogging of reservoir vent        -   Detection using inner pressure sensor (see 4.6 to 4.8)    -   2. clogging of pump controller vent only        -   The sensor membrane back side (which is not in contact with            the liquid) will be pressurized e.g. via the port (23) for            the inner detector (4), inducing a deflection of the            membrane and therefore a signal change. Positive            (respectively negative) pressure on the port (23) is            equivalent to a negative (resp. positive) pressure in the            pumping chamber (30).    -   3. clogging of all venting ports        -   The same pressure is observed in the reservoir and in the            pump controller, therefore the outer detector (13) membrane,            which is connected on one side with the patient and on the            other side with the pump controller, is able to detect any            pressure changes in the pump controller.

The clogging of the outlet valve port (24) only will be detected duringactuation if the cavity below the outlet valve is pressurized. Thispressure will induce an offset on the outlet valve opening threshold andthis offset can be detected according to the methods described in thedocument WO 2010/046728. This clogging is only possible during themounting of the pump controller onto the reservoir.

4.10. RESERVOIR FILLING MONITORING

The reservoir should be filled with a given quantity of liquid. In caseof overfilling, the device should prime the pump and actuate in order tolimit the pressure in the reservoir due to this overfilling.

The activation of the inner (4) and outer (13) detectors during thefilling is therefore useful to alarm the patient of any reservoiroverpressure using vibrations, visual or audible alarms.

Functional pumps are characterized in production. The equivalent fluidicresistance is determined with a criterion for the minimum value allowed.Since the pump has never been actuated between the production and thefilling, the minimum equivalent fluidic resistance is known. Themeasurement of the pressure during the filling gives therefore anindication of the flow rate through the pump. For very largeoverpressure, the valves open and the flowrate becomes driven by thecurve shown in FIG. 6.

The alarm is triggered when the pressure in the pumping chamber islarger than a predefined value. The alarm may be triggered continuouslyif the pressure remains larger than this predefined value and may bestopped only once the pressure is decreased below this predefined value.

The pressure release may be performed by the patient himself who caneither remove liquid by pulling on the syringe piston or simply byreleasing the syringe piston.

At the end of the filling, the pressure in the reservoir may be large incase of overfilling. The pressure is therefore monitored while the pumpis actuated continuously during the time necessary to reduce thepressure up to a predefined threshold value. The pump is then actuated apredefined number of cycles in order to ensure that the relativereservoir pressure is equal or very close to zero.

The invention claimed is:
 1. A medical device comprising a pumpingdevice, a pumping chamber, a sensor configured to measure a pressure inthe pumping chamber, a reservoir in fluid communication with the pumpingchamber, a notification device, and a processing unit configured tomonitor a signal of the pressure sensor during a filling of thereservoir when the pumping device is not actuated; wherein theprocessing unit is further configured to perform at least one of thefollowing steps: triggering a notification with the notification devicewhen a first threshold pressure signal is reached at the end ofreservoir filling; continuously actuating the pumping device to remove adetermined volume of fluid from the reservoir after the end of reservoirfilling.
 2. The medical device according to claim 1, wherein during thefilling the pumping device is in a rest position.
 3. The medical deviceaccording to claim 1, wherein the processing unit is further configuredto perform a step of stopping the triggering of the notification whenthe signal of the sensor is lower than a predefined threshold.
 4. Themedical device according to claim 1, wherein the processing unit isfurther configured to perform a step of stopping the step ofcontinuously actuating the pumping device when a predefined number ofstrokes have been reached by the step of continuously actuating.
 5. Themedical device according to claim 1, wherein the processing unit isfurther configured to perform a step of starting the continuouslyactuating after a predetermined time period after the end of thereservoir filling.
 6. The medical device according to claim 1, whereinthe processing unit is further configured to perform a step of stoppingthe continuously actuating when a predefined threshold for the signal ofthe sensor has been reached.
 7. The medical device according to claim 1,wherein the reservoir includes a predefined volume.
 8. The medicaldevice according to claim 1, wherein in the continuously actuating thepumping device, the determined volume of fluid is removed from thereservoir such that a volume of fluid remaining in the reservoir reachesa predefined value.
 9. The medical device according to claim 1, whereinthe pumping device further includes a pumping membrane, and the sensoris arranged to be in operative connection with the pumping membrane ofthe pumping chamber.
 10. The medical device according to claim 1,wherein the pumping device further includes a pumping membrane and anactuator for actuating the pumping membrane, wherein during the filling,the pumping membrane is in a rest position.
 11. The medical deviceaccording to claim 1, wherein the pumping device further includes apumping membrane and an actuator for actuating the pumping membrane,wherein during the filling, the actuator of the pumping membrane is notpowered.